AUGUST 2018 V O N I C H A N D H A K I M 2523 Hurricane Kinetic Energy Spectra from In Situ Aircraft Observations P. TRENT VONICH AND GREGORY J. HAKIM Department of Atmospheric Sciences, University of Washington, Seattle, Washington (Manuscript received 12 September 2017, in final form 22 April 2018) ABSTRACT Since the pioneering paper by Nastrom and Gage on aircraft-derived power spectra, significant progress has been made in understanding the wavenumber distribution of energy in Earth’s atmosphere and its implica- tions for the intrinsic limits of weather forecasting. Improvements in tropical cyclone intensity predictions have lagged those of global weather forecasting, and limited intrinsic predictability may be partially re- sponsible. In this study, we construct power spectra from aircraft data of over 1200 missions carried out by the National Oceanic and Atmospheric Administration (NOAA) and Air Force Reserve Command (AFRC) Hurricane Hunters. Each mission is parsed into distinct flight legs, and legs meeting a specified set of criteria are used for spectral analysis. Here, we produce power spectra composites for each category of the Saffir– Simpson scale, revealing a systematic relationship between spectral slope and storm intensity. Specifically, as storm intensity increases, we find that 1) spectral slope becomes steeper across scales from 10 to 160 km and 2) the transition zone where spectral slope begins to steepen shifts downscale. 1. Introduction predictability when p , 3, whereas systems governed by p $ 3 have unlimited predictability. While Lorenz The challenge of enhancing hurricane wind speed (1969) considered the predictability of flows within the forecasts is thought to involve several aspects of the two-dimensional vorticity equation framework, Rotunno modeling process. Rogers et al. (2013) succinctly sum- and Snyder (2008) applied Lorenz’s spectral approach to marized the issues in their aircraft-based hurricane in- the surface quasigeostrophic equations and confirmed vestigation, stating that the hurricane intensity skill that the structure of the energy spectrum strongly influ- shortfall exists within microphysical processes and pre- ences predictability. dictability constraints. Recent research connected with Observational documentation of large-scale atmo- the Hurricane Aerosol and Microphysics Program spheric spectra followed from the 1975–79 NASA-led (HAMP)—a sister project to the Hurricane Forecast Global Atmospheric Sampling Program. During this Improvement Project (HFIP)—supports the importance program, Boeing 747s fitted with special instrumenta- of microphysical processes to intensity forecasting tion gathered atmospheric data along commercial flight (Rosenfeld et al. 2007; Khain et al. 2010; Rosenfeld et al. paths, providing Nastrom and Gage (1985) with the data 2011). The fundamental forecasting limitations imposed to complete their seminal paper on wind and tempera- by hurricane predictability are not fully known, espe- ture power spectra. Their study yielded a power spec- cially from an observational perspective, which moti- 2 trum with a k 5/3 power law for wavelengths less than vates this paper on aircraft-based power spectra. 2 400 km and a k 3 power law for wavelengths larger than The study of atmospheric predictability revolves 400 km. These findings dispelled theories that—at the around the growth of errors. Given the power spectrum time—proposed a mesoscale energy gap. The continu- of a fluid flow, conclusions can be drawn as to how ous increase in energy from small to large scales dem- quickly small-scale errors will contaminate large scales. onstrated by Nastrom and Gage (1985) corroborated the Lorenz (1969) was the first to demonstrate this rela- findings of Lilly and Petersen (1983) and are consistent tionship, spurring research into the field of atmospheric with Vinnichenko (1970), Balsley and Carter (1982), and predictability that continues today. He demonstrated 2 Chen and Wiin-Nielsen (1978). While Nastrom and that systems governed by a k p power law have limited Gage (1985) provide an observational foundation for spectral properties of the extratropical upper tropo- Corresponding author: P. Trent Vonich, [email protected] sphere, the spectral properties of specific atmospheric DOI: 10.1175/JAS-D-17-0270.1 Ó 2018 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses). Unauthenticated | Downloaded 09/25/21 08:05 PM UTC 2524 JOURNAL OF THE ATMOSPHERIC SCIENCES VOLUME 75 features, such as hurricanes, remains an open question TABLE 1. Collection of mission statistics and power spectra results that we explore here. We note that the link between organized by storm intensity. properties of homogeneous and isotropic turbulence Flight Steepest Bin of steepest Mean and real atmospheric flows is complicated by inhomo- Category Missions legs slope slope (km) slope geneities, such as ubiquitous fronts and jet streams for 5 43 274 23.1 43–68 22.2 the extratropical spectrum and the primarily axisym- 4 120 760 22.4 43–68 22.0 metric circulation of hurricane vortices. Nevertheless, 3 114 718 22.5 68–106 22.0 documenting observed spectra provides a basis for com- 2 146 922 22.3 106–166 21.8 2 2 parison with numerical simulations (Skamarock 2004) 1 274 1597 2.1 68–106 1.8 TS 583 2973 21.9 43–68 21.7 and a source for theories that seek to explain observed phenomena. The goal of this paper is to document the observed speed data are output at 1 s as well and represent the av- spectrum of hurricanes using in situ aircraft observations. erage wind speed during a given second, where wind speeds Just as Nastrom and Gage (1985) created a climatology of are measured at a rate faster than 1 Hz. Both NOAA and wavenumber spectra for the upper troposphere, we AFRC wind data are adjusted for aircraft angle of attack present a climatology of wavenumber spectra for hurri- and sideslip angle. Wind speeds are recorded at the nearest canes as a function of the Saffir–Simpson scale. The re- knot for the AFRC and the nearest tenth of a meter mainder of the paper is structured as follows: In section 2, per second for NOAA. Additional detail regarding data we describe how the in situ aircraft observations are taken processing, data quality, and flight procedures can be and then discuss our methods for generating hurricane found in the appendix. spectra in section 3. Results are presented in section 4, For this study, we analyze data from tropical storms and we summarize our findings and ideas for future work (TSs) and hurricanes from 1980 to 2015, beginning with in section 5. Hurricane Allen and ending with Hurricane Patricia. After screening all available missions for quality and relevance (further explanation in section 3a), 1280 2. Data missions were found suitable for analysis. These 1280 missions are spread across 217 named storms, and a a. AFRC and NOAA Hurricane Hunters breakdown of their intensities is given in Table 1. Older Every hurricane season, the National Oceanic and missions—particularly those from the 53WRS in the Atmospheric Administration (NOAA) Hurricane 1980s and 1990s—do not include aircraft speed data. Hunters fly WP-3D aircraft from MacDill Air Force Base Selection of suitable missions and calculation of power (AFB), Florida, to conduct atmospheric reconnaissance spectra in the absence of aircraft speed are addressed in missions in the Atlantic basin and eastern North Pacific. section 3c. The U.S. Air Force Reserve Command (AFRC) operates b. NOAA best track data their own hurricane-hunting unit, the 53rd Weather Re- connaissance Squadron (53WRS), flying WC-130s out of To ensure a consistent sample, we require that flight Keesler AFB, Mississippi. Aircraft-mounted instruments legs pass through the radius of maximum wind (RMW) 2 record wind speed [64 knots (kt; 1 kt 5 0.51 m s 1)], wind to be considered for spectral analysis. Passing through direction (6108), GPS position [63 nautical miles (n mi; the RMW is useful for our analysis because this region of 1nmi5 1.85 km)], temperature, dewpoint, mixing ratio, the hurricane has the greatest inertial stability. Strong altitude, and other variables (Federal Coordinator for inertial stability makes the dynamics more barotropic, Meteorological Services and Supporting Research 2017). potentially steepening power spectra and influencing Missions analyzed in this study are separated into three predictability. To determine if a flight leg has intersected datasets: 1) NOAA 1-s data, 2) AFRC 1-s data, and 3) the RMW, NOAA best track (NBT) data were employed AFRC 10-s data. For flights occurring from 1960 to 2009, (detailed explanation in section 3b). Maximum 1-min sur- AFRC wind data are available at 10-s intervals, where face wind speed, minimum central pressure, and storm each wind value represents a trailing average of the wind position for North Atlantic and eastern Pacific storms are speed (53rd Weather Reconnaissance Squadron 2016). logged every 6 h by the National Hurricane Center. The After 2009, the 53WRS upgraded to 1-s data output; Joint Typhoon Warning Center accomplishes the same task however, each wind value in the AFRC 1-s dataset for the western Pacific, South Pacific, southern Indian, represents a 30-s average of the wind speed taking place and northern Indian. Occasionally the AFRC Hurricane during the 15 s before and after a specified time (53rd Hunters travel to the western Pacific during the North Weather Reconnaissance Squadron 2016). NOAA wind Atlantic’s dormant winter months, but the vast majority Unauthenticated | Downloaded 09/25/21 08:05 PM UTC AUGUST 2018 V O N I C H A N D H A K I M 2525 (.99%) of storms evaluated during this study are from the North Atlantic and eastern Pacific. 3. Methods a. Selecting suitable missions In this study, 1280 missions are considered. To distill all available missions into a set suitable for analysis, a subjec- tive screening method is applied.